1. Aims: To be able to find the inverse of a function. To know the graphical relationship between a function and its inverse. To understand the relationship between the domains and ranges of a function and its inverse. To know when it is possible to find an inverse function. (quadratics!) Functions Lesson 4

2. Finding inverse functions Recap We can find the inverse of a one-to-one function f ( x ) by ? Find the inverse of for -3 < x < 3 So the inverse function in terms of x is

3. Inverse functions How are the graphs of f ( x ) and f –1 ( x ) related? -3 3 -7 11 Domain is: -3 < x < 3 Range is: < y < Domain is: < x < Range is: < y < So the domain of f(x) is the _________________ of f -1 (x) And the range of f(x) is the _________________ of f -1 (x)

4. Try w/s

5. Quadratics Draw y = x 2 Why is this not a function? We can make it a function by restricting the domain to? What is the inverse? Draw it!

6. Finding inverse functions When finding the inverse of a general quadratics, we need to complete the square in order to find the solution. Find the inverse of,. Note the range of f(x) is y > So the domain of f -1 (x) will be x >

7. Try These